Textbook Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2x=64
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6. Exponential & Logarithmic Functions
Solving Exponential and Logarithmic Equations
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Solve the exponential equation.
A
17
B
34
C
8.5
D
0
Verified step by step guidance1
Start by recognizing that the equation is in the form of an exponential equation: \(100^x = 10^{x+17}\).
Express both sides of the equation with the same base. Note that \(100 = 10^2\), so rewrite the left side as \((10^2)^x = 10^{2x}\).
Now the equation becomes \(10^{2x} = 10^{x+17}\).
Since the bases are the same, set the exponents equal to each other: \(2x = x + 17\).
Solve for \(x\) by subtracting \(x\) from both sides to get \(x = 17\).
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